This paper studies the problem of routing in a multilayer (communication and social) network. Network protocols, such as link state routing and its variants, heavily used in mobile ad hoc networks (MANETs) cannot sustain robustness and efficiency as the topological information becomes easily stale with fast network dynamics. Attempts to collect and exchange excessive network information would result in significant overhead and would degrade the overall network performance. This paper presents the SCATE (Social-Cognitive Advancement at Tactical Edge) routing protocol that applies social-cognitive techniques to improve robustness and efficiency of a multilayer network with MANET communication and social links. In a distributed and decentralized setting with local information, nodes learn and update their distances to destinations using social-cognitive metrics and make routing decisions to minimize the end-to-end delay. The SCATE protocol is compared with Optimized Link State Routing (OLSR) with and without social links. Stand-alone computer simulations and high fidelity simulation/emulation tests with CORE and EMANE are used to evaluate SCATE under different communication network (traffic and mobility) and social network effects. Results show that the SCATE protocol is a viable solution to MANET routing by substantially reducing the overhead and the end-to-end delay, and increasing the end-to-end delivery ratio for both unicast and multicast traffic.